This invention concerns a process for designing a fuzzy regulator with at least one input parameter and at least one output parameter.
The principles of fuzzy regulators are described, for example, in the article xe2x80x9cFuzzy Controlxe2x80x94Heuristic Regulation by Means of Fuzzy Logicxe2x80x9d by Hans-Peter Preuxcex2, published in xe2x80x9catpxe2x80x9d (1992), no. 4, pages 176-183 and xe2x80x9catpxe2x80x9d (1992), no. 5, pages 239-246. The fuzzy regulators described there are used for open- and closed-loop control processes, for optimization of processes and for heuristic strategies by means of fuzzy logic. In fuzzy regulation, the fuzzy regulator may essentially have any desired number of input and output parameters.
To design a fuzzy regulator in accordance with the present invention, first the numerical value ranges of the input and output parameters are characterized qualitatively by linguistic values such as xe2x80x9csmall,xe2x80x9d xe2x80x9cmediumxe2x80x9d or xe2x80x9clarge.xe2x80x9d Each linguistic value is described by the membership function which quantifies the qualitative information provided by a linguistic value in such a manner that it yields a truth value for each numerical value occurring for a process parameter. Through this process, which is also known as fuzzification, the operating range of the process in question is divided into xe2x80x9cfuzzyxe2x80x9d sub-ranges. The number of sub-ranges corresponds to the number of linguistic values of an input parameter, or when there are several input parameters, the number of sub-ranges corresponds to the number of possible combinations of linguistic values of different input parameters. The control strategy is determined by IF-THEN rules for each of these sub-ranges or for several sub-ranges together. These rules are stored in a rule base. For each of these rules, a conclusion is given in the conditional part as a linguistic value whereby a combination of linguistic values of the input parameter may be provided, for example, by a linkage with the xe2x80x9cANDxe2x80x9d or xe2x80x9cORxe2x80x9d operators.
To calculate the truth value of the conditional part, the truth values obtained from the membership functions of the individual inputs are linked through the appropriate operators used in the rules. In the operation identified as xe2x80x9cinferencexe2x80x9d of calculating the conclusions for the individual rules, for example the membership function of the output parameters, named as the corresponding linguistic value in a rule, is limited to the truth value supplied by the conditional part of the rule. In the operation called xe2x80x9ccomposition,xe2x80x9d the effects of the rules concerning an output parameter are mutually superimposed, e.g. by forming the maximum of all membership functions of the output parameters. Finally, the calculation of the output parameter, referred to as xe2x80x9cdefuzzification,xe2x80x9d follows. This is done, for example, by calculating the position of the center of gravity of the surface defined by all the limited membership functions over the value range of the output parameters.
A rule base is incomplete if a rule is not expressly assigned to each of the aforementioned sub-ranges of the process. On the other hand, each linguistic value of the output parameter does not have to be specified in a rule as a conclusion. It is disadvantageous that output parameters that are unfavorable for the control may arise in operating states not covered by a rule.
An object of the present invention is to provide a process for a fuzzy regulator allowing an incomplete rule base to be supplemented in a simple manner and thus providing a fuzzy regulator that does not cause instabilities in the control circuit.
In fact, the truth value of the conditional part of the implicit rule is determined from the truth values of the conditional parts of the explicit rules by selecting the maximum value and forming the complement to the value 1 by using the equation:
Wj=1xe2x88x92max (Wi)
where
i=1, . . . , n, ixe2x89xa0j,
n=number of linguistic values of an output parameter and
wj=truth value of the implicit rule for the j-th linguistic value of the output parameter.
In addition, the truth value of the conditional part of the implicit rule is reduced by an evaluation factor. The truth value of the conditional part of the implicit rule may be linked to the truth value of the conditional part of another explicit rule.
Furthermore, the truth value of the conditional part of the implicit rule is linked to the truth value of the conditional part of one of the explicit rules, and the result of this linkage is used as its new truth value. With the new design process, a fuzzy regulator having favorable characteristics in the control circuit is available.